# Chapter 13 Properties of Solutions

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```					          Mass Percentage

mass of A in solution
Mass % of A =                         100
total mass of solution

Solutions
Parts per Million and
Parts per Billion
Parts per Million (ppm)
mass of A in solution
ppm =                         106
total mass of solution

Parts per Billion (ppb)
mass of A in solution
ppb =                         109
total mass of solution
Solutions
Mole Fraction (X)

moles of A
XA =
total moles in solution

• In some applications, one needs the
mole fraction of solvent, not solute—
make sure you find the quantity you
need!
Solutions
Molarity (M)

mol of solute
M=
L of solution

• You will recall this concentration
measure from Chapter 4.
• Because volume is temperature
dependent, molarity can change with
temperature.
Solutions
Molality (m)

mol of solute
m=
kg of solvent

Because both moles and mass do not
change with temperature, molality
(unlike molarity) is not temperature
dependent.
Solutions
Changing Molarity to Molality

If we know the
density of the
solution, we can
calculate the
molality from the
molarity, and vice
versa.

Solutions
Colligative Properties
• Changes in colligative properties
depend only on the number of solute
particles present, not on the identity of
the solute particles.
• Among colligative properties are
Vapor pressure lowering
Boiling point elevation
Melting point depression
Osmotic pressure                           Solutions
Vapor Pressure

Because of solute-
solvent intermolecular
attraction, higher
concentrations of
nonvolatile solutes
make it harder for
solvent to escape to
the vapor phase.

Solutions
Vapor Pressure

Therefore, the vapor
pressure of a solution
is lower than that of
the pure solvent.

Solutions
Raoult’s Law

PA = XAPA
where
• XA is the mole fraction of compound A
• PA is the normal vapor pressure of A at
that temperature

NOTE: This is one of those times when you
want to make sure you have the vapor
pressure of the solvent.                Solutions
Boiling Point Elevation and
Freezing Point Depression
Nonvolatile solute-
solvent interactions
also cause solutions
to have higher boiling
points and lower
freezing points than
the pure solvent.

Solutions
Boiling Point Elevation
The change in boiling
point is proportional to
the molality of the
solution:
Tb = Kb  m

where Kb is the molal
boiling point elevation
constant, a property of
Tb is added to the normal      the solvent.
Solutions
boiling point of the solvent.
Freezing Point Depression
• The change in freezing
point can be found
similarly:
Tf = Kf  m

• Here Kf is the molal
freezing point
depression constant of
the solvent.
Tf is subtracted from the normal
freezing point of the solvent.                          Solutions
Boiling Point Elevation and
Freezing Point Depression
Note that in both
equations, T does
Tb = Kb  m
not depend on what
the solute is, but
only on how many
particles are        Tf = Kf  m
dissolved.

Solutions
Colligative Properties of
Electrolytes
Since these properties depend on the number of
particles dissolved, solutions of electrolytes (which
dissociate in solution) should show greater changes
than those of nonelectrolytes.

Solutions
Colligative Properties of
Electrolytes
However, a 1 M solution of NaCl does not show
twice the change in freezing point that a 1 M
solution of methanol does.

Solutions
van’t Hoff Factor

One mole of NaCl in
water does not
really give rise to
two moles of ions.

Solutions
van’t Hoff Factor

Some Na+ and Cl−
reassociate for a
short time, so the
true concentration of
particles is
somewhat less than
two times the
concentration of
NaCl.
Solutions
The van’t Hoff Factor

• Reassociation is
more likely at higher
concentration.
• Therefore, the
number of particles
present is
concentration
dependent.

Solutions
The van’t Hoff Factor

We modify the
previous equations
by multiplying by the
van’t Hoff factor, i

Tf = Kf  m  i

Solutions
Osmosis
• Some substances form semipermeable
membranes, allowing some smaller
particles to pass through, but blocking
other larger particles.
• In biological systems, most
semipermeable membranes allow water
to pass through, but solutes are not free
to do so.
Solutions
Osmosis

In osmosis, there is net movement of solvent from
the area of higher solvent concentration (lower
solute concentration) to the are of lower solvent
concentration (higher solute concentration).        Solutions
Osmotic Pressure
• The pressure required to stop osmosis,
known as osmotic pressure, , is

n
=(         )RT = MRT
V
where M is the molarity of the solution

If the osmotic pressure is the same on both sides
of a membrane (i.e., the concentrations are the     Solutions
same), the solutions are isotonic.
Osmosis in Blood Cells

• If the solute
concentration outside
the cell is greater than
that inside the cell, the
solution is hypertonic.

• Water will flow out of
the cell, and crenation
results.
Solutions
Osmosis in Cells

• If the solute
concentration outside
the cell is less than
that inside the cell, the
solution is hypotonic.

• Water will flow into the
cell, and hemolysis
results.
Solutions
Molar Mass from
Colligative Properties
We can use the
effects of a colligative
property such as
osmotic pressure to
determine the molar
mass of a compound.

Solutions
Colloids:
Suspensions of particles larger than
individual ions or molecules, but too small to
be settled out by gravity.

Solutions
Tyndall Effect
• Colloidal suspensions
can scatter rays of light.
• This phenomenon is
known as the Tyndall
effect.

Solutions
Colloids in Biological Systems

Some molecules have
a polar, hydrophilic
(water-loving) end and
a nonpolar,
hydrophobic (water-
hating) end.

Solutions
Colloids in Biological Systems

Sodium stearate
is one example
of such a
molecule.

Solutions
Colloids in Biological Systems

These molecules
can aid in the
emulsification of fats
and oils in aqueous
solutions.

Solutions

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